Method for solving high PAPR problem of MCM communication system using unitary transform

ABSTRACT

The method contains the following steps. First, in a MCM system with N sub-carriers, the baseband signal blocks  X j   , j=1, 2, . . . ,B are supplemented with zeros and processed with LN-point IFFT, respectively, to obtain L-time oversampled time-domain signal blocks  x j   , j=1,2, . . . ,B. Then,  x j    undergoes Q Time Domain Circular Shifts or Frequency Domain Circular Shifts to obtain Q signal blocks {tilde over (x)} j   (i     j     ) , i j =1, Λ, Q. Subsequently, a B×B unitary transform is performed against (  x   1 , {tilde over (x)} 2   (i     2     ) , . . . , {tilde over (x)} B   (i     B     ) ). After the unitary transform, for each (i 2 , . . . , i B ) a combination having B time-domain signal blocks is obtained as follows: ({tilde over (y)} 1   (i     2     , . . . , i     B     ) , {tilde over (y)} 2   (i     2     , . . . , i     B     ) , . . . , {tilde over (y)} B   (i     2     , . . . ,i     B     ) )=(  x   1 , {tilde over (x)} 2   (i     2     ) , . . . , {tilde over (x)} B   (i     B     ) ) cU where U is the B×B unitary matrix, and c is an arbitrary constant (c≠0). Finally, the total Q B−1  combinations are compared against each other to select a best candidate for transmission that could produce the lowest peak value, or the smallest PAPR, or the lowest clipping noise power.

BACKKGROUND OF THE INVENTION

1. Field of the Invention

The present invention generally relates to multicarrier modulationsystems, and more particularly to a method for solving the highpeak-to-average power ratio problem of multicarrier modulation system.

2. The Related Arts

Multicarrier modulation (MCM) systems, such as those adopting orthogonalfrequency division multiplexing (OFDM) modulation/demodulationtechniques, have been widely applied in digital subscriber loop (DSL),digital video broadcasting (DVB), digital audio broadcasting (DAB), andwireless local area network (WLAN), due to their high spectralefficiency, better immunity to multi-path fading, easier equalization tofrequency-selective fading channels.

However, in contrast to single-carrier modulation systems, MCM systemshave an inherent disadvantage. That is, the time-domain signal of a MCMsystem usually suffer high peak-to-average power ratio (PAPR). In a MCMsystem, as various data are transmitted simultaneously over varioussub-carriers, the total effect of these sub-carriers would result in atime-domain signal and a high PAPR where the peak value is significantlygreater than the average value. Due to the high PAPR, the poweramplifier of a MCM system's transmitter has to be designed with anenlarged linear region. However, the design of such a power amplifier isnot an easy task. On the other hand, if a power amplifier of limitedlinear region is adopted in the MCM system's transmitter, the poweramplifier would sometimes operate in the non-linear region (i.e., undersaturation). This mode of operation would inevitably cause non-lineardistortion.

Therefore, quite a few methods have been disclosed in reducing a MCMsystem's PAPR. Among them, selective mapping (SLM) is a quite popularapproach (please see R. W. Bauml, R. F. H. Fischer, J. B. Huber,“Reducing the peak-to-average power ratio of multicarrier modulation byselected mapping, “Electronic Letters, vol. 32, pp. 2056-2057, 1996, andM. Breiling, S. H. Müller-Weinfurtner, and J. B. Huber, “SLM peak-powerreduction without explicit side information,” IEEE CommunicationsLetters, vol. 5, no. 6, pp. 239-241, June 2001). The basic idea behindSLM is that, when multiple modulation signals have the same phase, ahigh time-domain peak value would be resulted. Therefore, by adjustingsome of the modulation signals' phases, the peak value could be reduced.A conventional approach using SLM is shown in FIG. 1 which produces Qcandidates. Then, a best candidate such as one that could produce thelowest PAPR is selected. As illustrated, the conventional methodrequires Q inverse fast Fourier transforms (IFFTs) and each IFFTrequires highly complicated computation. In addition, a high Q value isrequired to effectively reduce the PAPR. These all contribute to theimplementation complexity of SLM.

Accordingly, there are teachings using unitary transforms to producemultiple candidates for the reduction of PAPR (please see Heechoon Lee,Daniel N. Liu, Weijun Zhu and Michael P. Fitz, “Peak Power ReductionUsing a Unitary Rotation in Multiple Transmit Antennas” 2005 IEEEInternational Conference on Communications, Seoul, Korea, May 16-20,2005). However, the unitary transform matrices U still requires rathersignificant computation and therefore still has substantialimplementation difficulty, where

${U = \begin{pmatrix}r & {\sqrt{1 - r^{2}}{\mathbb{e}}^{j\theta}} \\{\sqrt{1 - r^{2}}{\mathbb{e}}^{- {j\theta}}} & {- r}\end{pmatrix}},{0 \leq r \leq 1},{0 \leq \theta \leq {2\pi}}$

BRIEF SUMMARY OF THE INVENTION

Accordingly, the present invention provides a novel method to solve thehigh PAPR problem of MCM systems.

The method contains the following steps. First, in a MCM system with Nsub-carriers, the baseband signal blocks X_(j) , j=1, 2, . . . , B aresupplemented with zeros and processed with LN-point IFFT, respectively,to obtain L-time oversampled time-domain signal blocks x_(j) , j=1,2, .. . ,B. Then, x_(j) undergoes Q Time Domain Circular Shifts or FrequencyDomain Circular Shifts to obtain Q signal blocks {tilde over (x)}_(j)^((i) ^(j) ⁾, i_(j)=1, Λ, Q. Subsequently, a B×B unitary transform isperformed against ( x ₁, {tilde over (x)}₂ ^((i) ² ⁾, . . . , {tildeover (x)}_(B) ^((i) ^(B) ⁾). After the unitary transform, for each (i₂,. . . ,i_(B)), a combination having B time-domain signal blocks isobtained as follows: ({tilde over (y)}₁ ^((i) ² ^(, . . . , i) ^(B) ⁾,{tilde over (y)}₂ ^((i) ² ^(, . . . , i) ^(B) ⁾, . . . , {tilde over(y)}_(B) ^((i) ² ^(, . . . , i) ^(B) ⁾=( x ₁, {tilde over (x)}₂ ^((i) ²⁾, . . . , {tilde over (x)}_(B) ^((i) ^(R) ⁾) cU where U is the B×Bunitary matrix, and c is an arbitrary constant (c≠0). Finally, the totalQ^(B−1) combinations are compared against each other to select a bestcandidate for transmission that could produce the lowest peak value, orthe smallest PAPR, or the lowest clipping noise power.

The method adopts the concept of SLM but avoids the conventional SLM'sdrawback of using a large number of IFFTs. The method therefore has asignificantly less complexity in effectively reducing the PAPR or theclipping noise power resulted from a high PAPR of a MCM system withoutsacrificing error rate.

The foregoing and other objects, features, aspects and advantages of thepresent invention will become better understood from a careful readingof a detailed description provided herein below with appropriatereference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic structure diagram of a system using a conventionalSLM.

FIG. 2 is a schematic structure diagram of a system using a firstembodiment of the present invention.

FIG. 3 is a schematic structure diagram of a system using a secondembodiment of the present invention.

FIG. 4 is a schematic structure diagram of a system using a thirdembodiment of the present invention.

FIG. 5 shows the simulation results of Complementary CumulativeDistribution Function (CCDF) of systems using SS-CARI and the presentinvention, respectively.

DETAILED DESCRIPTION OF THE INVENTION

The following descriptions are exemplary embodiments only, and are notintended to limit the scope, applicability or configuration of theinvention in any way. Rather, the following description provides aconvenient illustration for implementing exemplary embodiments of theinvention. Various changes to the described embodiments may be made inthe function and arrangement of the elements described without departingfrom the scope of the invention as set forth in the appended claims.

FIG. 2 is a schematic diagram showing a first embodiment of the presentinvention, which performs 2×2 unitary transforms for a MCM system havingN (N≧2) sub-carriers.

First in step 1, in order to achieve more accurate estimation of thePAPR, the present embodiment supplements (L−1)N zeros (L≧1) to thebaseband signal blocks X₁ =(X_(1,0), X_(1,1), . . . , X_(1,N−1)) and X₂=(X_(2,0), X_(2,1), . . . , X_(2,N−1)) generated from the MCM systemwith N sub-carriers, respectively, so that X₁ and X₂ become (X_(1,0),X_(1,1), . . . , X_(1,N−1), 0, . . . , 0) and (X_(2,0), X_(2,1), . . . ,X_(2,N−1), 0, . . . , 0).

The baseband signal blocks X₁ and X₂ then undergo LN-point IFFT (denotedas “LN-pt IFFT” in the drawing), respectively, to obtain L-timeoversampled time-domain signal blocks x₁ =(x_(1,0), x_(1,1), . . . ,x_(1,LN−1)) and x₂ =(x_(2,0), x_(2,1), . . . , x_(2,LN−1)).

Subsequently, in step 2, x₂ undergoes Q (Q≧1) different Time DomainCircular Shift with parameters τ₁, τ₂, . . . , τ_(Q) (all greater thanzero) to obtain {tilde over (x)}₂ ^((i)=TS( x) ₂, τ_(i))=(a_(2,1)^((i)), a_(2,2) ^((i)), . . . , a_(2,n) ^((i))), i=1, . . . ,Q . TheTime Domain Circular Shift operation TS( x ₂, τ_(i)) is to shift thetime-domain signal block x₂ left for τ_(i) (τ_(i) is any integer) timepoints or more specifically,a _(2,n) ^((i)) =x _(2,[(n−τ) _(i) _()mod(LN)]) , n=0, 1, . . . , (LN−1)where “mod” is the standard modulo operation.

Then in step 3, for each i, a 2×2 unitary transform is performed against( x₁ , {tilde over (x)}₂ ^((i))). Please note that a characteristic ofthe unitary transform is that the energy of a signal block before andafter the unitary transform remains unchanged. After the unitarytransforms, for each i, a combination having two time-domain signalblocks ({tilde over (y)}₁ ^((i)), {tilde over (y)}₂ ^((i)))is obtained.In other words,({tilde over (y)} ₁ ^((i)) , {tilde over (y)} ₂ ^((i)))=( x ₁ , {tildeover (x)} ₂ ^((i)))Uwhere U is the 2×2 unitary matrix. To reduce computational complexity,the following unitary matrix U could be adopted:

$U = \begin{pmatrix}{1/\sqrt{2}} & {1/\sqrt{2}} \\{1/\sqrt{2}} & {{- 1}/\sqrt{2}}\end{pmatrix}$In implementation, it is also possible to adopt ({tilde over (y)}₁^((i)), {tilde over (y)}₂ ^((i)))=( x₁ , {tilde over (x)}₂ ^((i)))cU,where c is an arbitrary constant (c≠0). Therefore, if

${{cU} = \begin{pmatrix}1 & 1 \\1 & {- 1}\end{pmatrix}},$multiplication could be avoided and the computational complexity isextremely low.

Finally, in step 4, all Q combinations ({tilde over (y)}₁ ⁽¹⁾, {tildeover (y)}₂ ⁽¹⁾), ({tilde over (y)}₁ ⁽²⁾, {tilde over (y)}₂ ⁽²⁾), . . . ,and ({tilde over (y)}₁ ^((Q)), {tilde over (y)}₂ ^((Q))) are comparedagainst each other and a best combination ({tilde over (y)}₁ ⁽¹⁾, {tildeover (y)}₂ ⁽¹⁾) is selected for transmission.

The condition for deciding the best combination could be that ({tildeover (y)}₁ ^((l)), {tilde over (y)}₂ ^((l))) produces the lowest peakvalue, or ({tilde over (y)}₁ ^((l)), {tilde over (y)}₂ ^((l))) producesthe smallest PAPR. The two selection criteria would sometimes producedifferent results. If the condition is the lowest peak value, the IFFTof L-time oversampling used should have the L value at least 4 so thatthe L-time oversampling result would closely approximate the PAPR ofcontinuous-time signal.

In addition, the condition could also be that ({tilde over (y)}₁ ^((l)),{tilde over (y)}₂ ^((l))) produces the lowest clipping noise power. Theso-called clipping refers to the following function that turns an inputsignal x into an output signal g(x):

x = p 𝕖^(jΦ), p = x ${g(x)} = \left\{ \begin{matrix}{x,} & {{{for}\mspace{14mu} p} \leq A} \\{{A\;{\mathbb{e}}^{j\Phi}},} & {{{for}\mspace{14mu} p} > A}\end{matrix} \right.$Using the time-domain signal block x=(x₀, x₁, . . . , LN−1) as example,its clipping noise power would be

$\sum\limits_{i = 0}^{{LN} - 1}{{{x_{i} - {g\left( x_{i} \right)}}}^{2}.}$The A value could be adjusted in accordance with power backoff and it isrelated to the multiple L in oversampling and number of sub-carriers N.

When the lowest clipping noise power is the condition for selection,there is not much difference between the produced clipping noise usingL=1, 2, or 4. As such, implementation could adopt an IFFT using theNyquist Rate (i.e., L=1) which could further reduce the implementationcomplexity.

FIG. 3 is a schematic diagram showing a second embodiment of the presentinvention, which performs circular shift in the frequency domain incontrast to the circular shift in the time domain performed by theprevious embodiment.

Step 1 is identical to the previous embodiment and (L−1)N zeros (L≧1)are supplemented to the baseband signal blocks X₁ =(X_(1,0), X_(1,1), .. . , X_(1,N−1)) and X₂ =(X_(2,0), X_(2,1), . . . , X_(2,N−1)) generatedfrom the MCM system with N sub-carriers, respectively, so that X₁ and X₂become (X_(1,0), X_(1,1), . . . , X_(1,N−1), 0, . . . , 0) and (X_(2,0),X_(2,1), . . . , X_(2,N−1), 0, . . . , 0). The baseband signal blocks X₁and X₂ then undergo LN-point IFFT (denoted as “LN-pt IFFT” in thedrawing), respectively, to obtain L-time oversampled time-domain signalblocks x₁ =(x_(1,0), x_(1,1), . . . , x_(1,LN−1)) and x₂ =(x_(2,0),x_(2,1), . . . , x_(2,LN−1)).

Then, in step 2, x₂ is processed by the following function for Q timessequentially:b _(2,n) ^((i)) =x _(2,n) e ^(−j2roiκ) ^(i) ^(/LN) , n=0, 1, Λ,(LN−1),i=1, . . . , QThe function is equivalent to subjecting frequency-domain signal block(X_(2,0), X_(2,1), . . . , X_(2,N−1), 0, . . . , 0) to Q differentFrequency Domain Circuit Shift to obtain time-domain signals:{tilde over (x)} ₂ ^((i)) =FS((X _(2,0) , X _(2,1) , . . . , X _(2,N−1),0, . . . , 0), κ_(i))=(b _(2,1) ^((i)) , b _(2,2) ^((i)) , . . . , b_(2,n) ^((i))), i=1, Λ, QIn other words, FS((X_(2,0), X_(2,1), . . . , X_(2,N−1), 0, . . . , 0),κ_(i)) is the corresponding time-domain signal block after shifting thefrequency-domain signal block (X_(2,0), X_(2,1), . . . , X_(2,N−1), 0, .. . , 0) to the left κ_(i)(κ_(i) is an arbitrary integer) frequencyunits.

Subsequently, in step 3, for each i, the 2×2 unitary transform identicalto that used in the previous embodiment is performed against ( x₁ ,{tilde over (x)}₂ ^((i))). After the unitary transforms, for each i, acombination having two time-domain signal blocks ({tilde over (y)}₁^((i)), {tilde over (y)}₂ ^((i))) is obtained.

Finally, in step 4, all Q combinations ({tilde over (y)}₁ ⁽¹⁾, {tildeover (y)}₂ ⁽¹⁾), ({tilde over (y)}₁ ⁽²⁾, {tilde over (y)}₂ ⁽²⁾), . . . ,and ({tilde over (y)}₁ ^((Q)), {tilde over (y)}₂ ^((Q))) are comparedagainst each other and a best combination ({tilde over (y)}₁ ⁽¹⁾, {tildeover (y)}₂ ⁽¹⁾) is selected for transmission. The condition for decidingthe best combination, identical to the previous embodiment, could bethat ({tilde over (y)}₁ ⁽¹⁾, {tilde over (y)}₂ ⁽¹⁾) produces the lowestpeak value, or ({tilde over (y)}₁ ⁽¹⁾, {tilde over (y)}₂ ⁽¹⁾) producesthe smallest PAPR, or ({tilde over (y)}₁ ⁽¹⁾, {tilde over (y)}₂ ⁽¹⁾)produces the lowest clipping noise power.

Compared to Time Domain Circular Shift, the Frequency Domain CircularShift is more complex in that calculating b_(2,n) ^((i)=x)_(2,n)e^(−j2πnκ) ^(l) ^(/LN) from x_(2,n) requires more computation thancaculating a_(2,n) ^((i))=x_(2,[(n−τ) _(i) _()mod(LN)]) from x_(2,n). Inaddition, when the oversampling factor L is greater than 1, usingFrequency Domain Circular Shift would also result in the out-of-bandspectrum.

In the following, the present invention is extended from processing twomulticarrier modulation signal blocks to processing B (B≧2) signalblocks. For simplicity, the embodiments presented use Time DomainCircular Shift only as they could be easily extended to cover FrequencyDomain Circular Shift cases following the foregoing description.

As illustrated in FIG. 4, in step 1, B baseband signal blocks X₁=(X_(1,0), X_(1,1), . . . , X_(1,N−1)), X ₂=(X_(2,0), X_(2,1), . . . ,X_(2,N−1)), . . . , X _(B)=(X_(B,0), X_(B,1), . . . , X_(B,N−1))generated from the MCM system with N sub-carriers are supplemented withzeros and processed with LN-point IFFT, respectively, to obtain L-timeoversampled time-domain signal blocks x₁ =(x_(1,0), x_(1,1), . . . ,x_(1,LN−1)), x₂ =(x_(2,0), x_(2,1), . . . , x_(2,LN−1)), . . . , x_(B)=(x_(B,0), x_(B,1), . . . , x_(B,LN−1)).

Then, in step 2, x_(j) undergoes Q Time Domain Circular Shifts withparameters τ_(j,1), τ_(j,2), . . . , τ_(j,Q) to obtain {tilde over(x)}_(j) ^((i))=TS( x _(j),τ_(j,1)), i=1, Λ, Q, j=2, Λ, B.

Subsequently, in step 3, a B×B unitary transform is performed against (x ₁, {tilde over (x)}₂ ^((i) ² ⁾, . . . , {tilde over (x)}_(B) ^((i)^(B) ⁾). After the unitary transform, for each (i₂, . . . , i_(B)), acombination having B time-domain signal blocks is obtained as follows:({tilde over (y)} ₁ ^((i) ² ^(, . . . , i) ^(B) ⁾ , {tilde over (y)} ₂^((i) ² ^(, . . . , i) ^(B) ⁾ , . . . , {tilde over (y)} _(B) ^((i) ²^(, . . . , i) ^(B) ⁾)=( x ₁ , {tilde over (x)} ₂ ^((i) ² ⁾ , . . . ,{tilde over (x)} _(B) ^((i) ^(B) ⁾)c Uwhere U is the B×B unitary matrix, and c is an arbitrary constant (c≠0).

Finally, in step 4, for all (i₂, . . . , i_(B)) combinations, thecombinations ({tilde over (y)}₁ ^((i) ² _(, . . . ,i) ^(B) ₎,{tilde over(y)}₂ ^((i) ² ^(, . . . , i) ^(B) ⁾, . . . , {tilde over (y)}_(B) ^((i)² ^(, . . . , i) ^(B) ⁾), i₂=1, Λ, Q, . . . , i_(B)=1, Λ, Q are comparedagainst each other to select a best combination ({tilde over (y)}₁ ^((i)² ^(, . . . , i) ^(B) ⁾, {tilde over (y)}₂ ^((i) ² ^(, . . . , i) ^(B)⁾, . . . , {tilde over (y)}_(B) ^((i) ² ^(, . . . , i) ^(B) ⁾) fortransmission. The condition for deciding the best combination, identicalto the previous embodiments, could be the combination that produces thelowest peak value, or the smallest PAPR, or the lowest clipping noisepower.

The foregoing embodiments all perform a single unitary transform. In thefollowing, the present invention is extended to cover embodimentsperforming P unitary transforms (P≧1).

In step 1, B baseband signal blocks X ₁=(X_(1,0), X_(1,1), . . . ,X_(1,N−1)), X ₂=(X_(2,0), X_(2,1), . . . , X_(2,N−1)), . . . , X_(B)=(X_(B,0), X_(B,1), . . . , X_(B,N−1)) are supplemented with zerosare processed with LN-point IFFT, respectively, to obtain L-timeoversampled time-domain signal blocks x₁ =(x_(1,0), x_(1,1), . . . ,x_(1,LN−1)), x₂ =(x_(2,0), x_(2,1), . . . , x_(2,LN−1)), . . . , x_(B)=(x_(B,0), x_(B,1), . . . , x_(B,LN−1)).

Then, in step 2, x_(j) undergoes Q Time Domain Circular Shifts withparameters τ_(j,1), τ_(j,2), . . . , τ_(j,Q) to obtain {tilde over(x)}_(j) ^((i))=TS( x _(j), τ_(j,i)), i=1, Λ, Q, j=2, Λ, B.

Subsequently, in step 3, P B×B unitary transforms are performed against( x ₁, {tilde over (x)}₂ ^((i) ² ⁾, . . . , {tilde over (x)}_(B) ^((i)^(B) ⁾). After the pth unitary transforms, p=1, 2, . . . , P, for each(i₂, . . . , i_(B)), a combination having B time-domain signal blocks isobtained as follows:({tilde over (y)} ₁ ^((i) ² ^(, . . . , i) ^(B) ⁾ , {tilde over (y)} ₂^((i) ² ^(, . . . , i) ^(B) ⁾ , . . . , {tilde over (y)} _(B) ^((i) ²^(, . . . , i) ^(B) ⁾)=( x ₁ , {tilde over (x)} ₂ ^((i) ² ⁾ , . . . ,{tilde over (x)} _(B) ^((i) ^(B) ⁾) c U _(p)where U_(p) is the B×B unitary matrix, and c is an arbitrary constant(c≠0).

Finally, in step 4, for all (i₂, . . . ,i_(B)) combinations (there aretotal PQ^(B−1) combinations), the combinations ({tilde over (y)}₁ ^((i)² ^(, . . . , i) ^(B,p) ⁾, {tilde over (y)}₂ ^((i) ² ^(, . . . , i)^(B,p) ⁾, . . . , {tilde over (y)}_(B) ^((i) ² ^(, . . . , i) ^(B,p) ⁾),i₂=1, Λ, Q, . . . , i_(B)=1, Λ, Q, p=1, . . . , P are compared againsteach other to select a best combination for transmission. The conditionfor deciding the best combination, identical to the previousembodiments, could be the combination that produces the lowest peakvalue, or the smallest PAPR, or the lowest clipping noise power.

In the following, the performances of the present invention and a SLMcalled SS-CARI (Successive Suboptimal CARI) (please see Z. M. Tan and Y.Bar-Ness, “STBC MIMO-OFDM Peak Power Reduction by Cross-antenna Rotationand Inversion,” IEEE Commun. Lett., vol. 9, pp. 592, July 2005) arecompared as they are used in a two-input and two-output (2×2) QPSK OFDMMCM (MIMO-OFDM) system with 128 sub-carriers.

When reducing PAPR using SS-CARI, if the number of candidates is 8 or16, correspondingly 16 or 32 IFFTs have to be conducted. In contrast,only two IFFTs are required for the present invention, whether thenumber of circular shifts is 8 or 16 (i.e., Q=8 or 16 so as to produce 8or 16 candidates).

Simulation results for the foregoing system's Complementary CumulativeDistribution Function (CCDF) using SS-CARI and the present invention areshown in the graph of FIG. 5 where the curves marked as TDCS are thoseusing Time Domain Circular Shift. As illustrated, whether the number ofcandidates is 8 or 16, the present invention has lower CCDF compared toSS-CARI. In other words, the present invention indeed could effectivelyreduce the PAPR with significantly less complexity. Also from simulationdata, the present invention has an error rate comparable to that ofSS-CARI. The present invention therefore does not achieve the reductionof PAPR at the cost of the system's error rate.

Although the present invention has been described with reference to thepreferred embodiments, it will be understood that the invention is notlimited to the details described thereof. Various substitutions andmodifications have been suggested in the foregoing description, andothers will occur to those of ordinary skill in the art. Therefore, allsuch substitutions and modifications are intended to be embraced withinthe scope of the invention as defined in the appended claims.

1. A method for solving high peak-to-average power ratio (PAPR) problemof a multicarrier modulation (MCM) system with N sub-carriers,comprising the steps of: supplementing baseband signal blocks X_(j)=(X_(j,0), X_(j,1), . . . , X_(j,N−1)), j=1, 2, . . . , B generatedfrom the MCM system with (L−1)N zeros and processing X _(j)=(X_(j,0),X_(j,1), . . . , X_(j,N−1), 0, . . . , 0) with LN-point IFFT to obtainL-time oversampled time-domain signal blocks x _(j)=(x_(j,0), x_(j,1), .. . , x_(j, LN−1)), respectively; performing a circular shift operationon x _(j) to obtain Q signal blocks {tilde over (x)}_(j) ^((i) ^(j) ⁾,i_(j)=1, . . . , Q; for ( x₁ , {tilde over (x)}₂ ^((i) ² ⁾, . . . ,{tilde over (x)}_(B) ^((i) ^(B) ⁾), i₂=1, . . . , Q, . . . , i_(B)=1, .. . , Q, performing P B×B unitary transform using matrixes Up, p=1, . .. , P to obtain, for each (i₂, . . . , i_(B), p) combination, acombination containing B time-domain signal blocks ({tilde over (y)}₁^((i) ² ^(, . . . , i) ^(B) ^(, p)), {tilde over (y)}₂ ^((i) ²^(, . . . , i) ^(B) ^(, p)), . . . ,{tilde over (y)}_(B) ^((i) ²^(, . . . , i) ^(B) ^(, p)))=( x₁ , {tilde over (x)}₂ ^((i) ² ⁾, . . . ,{tilde over (x)}_(B) ^((i) ^(B) ⁾) cU_(p) where c is an arbitraryconstant (c≠0); and for all PQ^(B−1) combinations, comparing saidcombinations ({tilde over (y)}₁ ^((i) ² ^(, . . . , i) ^(B) ^(, p)),{tilde over (y)}₂ ^((i) ² ^(, . . . , i) ^(B) ^(, p)), . . . , {tildeover (y)}_(B) ^((i) ² ^(, . . . , i) ^(B) ^(, p))), i₂=1, . . . , Q, . .. , i_(B)=1, . . . , Q, p=1, . . . , P to select a best combination({tilde over (y)}₁ ^((i) ² ^(, . . . , i) ^(B) ^(, p)), {tilde over(y)}₂ ^((i) ² ^(, . . . , i) ^(B) ^(, p)), . . . , {tilde over (y)}_(B)^((i) ² ^(, . . . , i) ^(B) ^(, p))) for transmission.
 2. The methodaccording to claim 1, wherein said best combination ({tilde over (y)}₁^((i) ² ^(, . . . , i) ^(B) ⁾, {tilde over (y)}₂ ^((i) ² ^(, . . . , i)^(B) ⁾, . . . , {tilde over (y)}_(B) ^((i) ² ^(, . . . , i) ^(B) ⁾)achieves the lowest peak value.
 3. The method according to claim 1,wherein said best combination ({tilde over (y)}₁ ^((i) ² ^(, . . . , i)^(B) ⁾, {tilde over (y)}₂ ^((i) ² ^(, . . . , i) ^(B) ⁾, . . . , {tildeover (y)}_(B) ^((i) ² ^(, . . . , i) ^(B) ⁾) achieves the smallest PAPR.4. The method according to claim 1, wherein said best combination({tilde over (y)}₁ ^((i) ² ^(, . . . , i) ^(B) ⁾, {tilde over (y)}₂^((i) ² ^(, . . . , i) ^(B) ⁾, . . . , {tilde over (y)}_(B) ^((i) ²^(, . . . ,i) ^(B) ⁾) achieves the lowest clipping noise power.
 5. Themethod according to claim 1, wherein L=1.
 6. The method according toclaim 1, wherein said circular shift operation is to shift x_(j) to theleft for τ_(i) _(j) time points to obtain time-domain signal block{tilde over (x)}_(j) ^((i) ^(j) ⁾, i_(j)=1, . . . , Q as follows:{tilde over (x)} _(j) ^((i) ^(j) ⁾=(a _(j,0) ^((i) ^(j) ⁾ , a _(j,1)^((i) ^(j) ⁾ , . . . , a _(j,LN−1) ^((i) ^(j) ⁾); anda _(j,n) ^((i) ^(j) ⁾ =x _(j,[(n−τ) _(ij) _()mod(LN)]) , n=0,1, . . . ,(LN−1), i _(j)=1, . . . , Q, j=2, . . . , B.
 7. The method according toclaim 1, wherein said circular shift operation is to shift x _(j) 'sfrequency-domain signal block (X_(j,0), X_(j,1), . . . , X_(j,N−1), 0, .. . , 0) to the left for κ_(i) _(j) frequency units to obtaincorresponding time-domain signal block {tilde over (x)}_(j) ^((i) ^(j) ⁾as follows:{tilde over (x)} _(j) ^((i) ^(j) ⁾=(b _(j,0) ^((i) ^(j) ⁾ , b _(j,1)^((i) ^(j) ⁾ , . . . , b _(j,LN−1) ^((i) ^(j) ⁾); andb _(j,n) ^((i) ^(j) ⁾ =x _(j,n) e ^(−j2πnκ) ^(ij) ^(/LN) , n=0,1, . . ., (LN−1), i _(j)=1, . . . , Q, j=2, . . . , B.